Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Symmetries of the Energy-Momentum Tensor for Static Plane Symmetric Spacetimes

Version 1 : Received: 21 July 2023 / Approved: 21 July 2023 / Online: 21 July 2023 (09:34:39 CEST)

A peer-reviewed article of this Preprint also exists.

Khan, F.; Ullah, W.; Hussain, T.; Sumelka, W. Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes. Symmetry 2023, 15, 1614. Khan, F.; Ullah, W.; Hussain, T.; Sumelka, W. Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes. Symmetry 2023, 15, 1614.

Abstract

This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress-energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy-momentum tensor is nondegenerate and degenerate. For the case of degenerate energy-momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy-momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy-momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress-energy.

Keywords

Matter collineations; Static Plane-Symmetric Spacetimes; Contravariant and Mixed Energy-Momentum Tensor

Subject

Physical Sciences, Mathematical Physics

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